Relativistic momentum and conservation of this

In summary, the conversation discusses a collision between two particles, resulting in a joined particle. The equations for conservation of momentum and energy are used to find the speed and mass of the joined particle. It is determined that the mass is 2m and the speed is (4/5)c.
  • #1
Niles
1,866
0

Homework Statement


A particle with mass m and speed (4/5)c collides with a particle (with mass m as well, but speed = 0) un-elastically, and continues as one particle.

I have to find the speed and mass for this "joined" particle.

The Attempt at a Solution



Ok, first - conservation of momentum!

1) I use that gamma_1*m*(4/5)c + 0 = gamma_2*M*v

2) I also use gamma_1*m + m = gamma_2*M

Is this correct? In the notes I took in class today, I wrote this for #1: gamma_1*m*(4/5)c + 0 = gamma_2*M - but I guess I wrote this one down wrong?

Thank for you all in advance.
 
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  • #2
Niles said:

Homework Statement


A particle with mass m and speed (4/5)c collides with a particle (with mass m as well, but speed = 0) un-elastically, and continues as one particle.

I have to find the speed and mass for this "joined" particle.

The Attempt at a Solution



Ok, first - conservation of momentum!

1) I use that gamma_1*m*(4/5)c + 0 = gamma_2*M*v

2) I also use gamma_1*m + m = gamma_2*M

Is this correct? In the notes I took in class today, I wrote this for #1: gamma_1*m*(4/5)c + 0 = gamma_2*M - but I guess I wrote this one down wrong?

Thank for you all in advance.

Your equations 1 and 2 are correct. Note that gamma_1 is known so that leaves two unknowns: M and v.
 
  • #3
Great, thanks!
 
  • #4
M=2m. Then gamma2 cancels out of the equation for v,
 

FAQ: Relativistic momentum and conservation of this

What is relativistic momentum?

Relativistic momentum is a concept in physics that takes into account the effects of special relativity on an object's momentum. It is given by the formula p = mv/√(1-v^2/c^2), where p is momentum, m is mass, v is velocity, and c is the speed of light.

How is relativistic momentum different from classical momentum?

Unlike classical momentum, which is defined as mv, relativistic momentum takes into account the relationship between an object's velocity and the speed of light. This becomes significant at high velocities, such as those close to the speed of light, where classical momentum would give inaccurate results.

What is the conservation of relativistic momentum?

The conservation of relativistic momentum states that the total relativistic momentum of a closed system remains constant, regardless of any interactions or changes within the system. This is similar to the conservation of classical momentum, but it takes into account the relativistic effects on momentum.

How does relativistic momentum affect the behavior of particles at high speeds?

At high speeds, relativistic momentum causes particles to behave differently than they would at lower speeds. For example, as an object's velocity approaches the speed of light, its relativistic momentum increases significantly while its classical momentum remains constant. This can result in changes in an object's mass, energy, and trajectory.

Can relativistic momentum be applied to all types of particles?

Yes, relativistic momentum is a fundamental concept in physics and can be applied to all types of particles, including subatomic particles and massive objects like planets. It is especially important in fields such as particle physics and astrophysics, where the effects of high velocities and the speed of light are significant.

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